﻿ Engineering Entrance Exam Question and Answers | Probability - Zigya

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# Probability

#### Multiple Choice Questions

81.

The probability distribution of a random variable X is given below
 X = x 0 1 2 3 P(X) = x $\frac{1}{10}$ $\frac{2}{10}$ $\frac{3}{10}$ $\frac{4}{10}$

Then the variance of X is

• 1

• 2

• 3

• 4

82.

The probability that an individual suffers a bad reaction from an injection is 0.001. The probability that out of 2000 individuals exactly three will suffer bad reaction is

• $\frac{1}{{\mathrm{e}}^{2}}$

• $\frac{2}{3{\mathrm{e}}^{2}}$

• $\frac{8}{3{\mathrm{e}}^{2}}$

• $\frac{4}{3{\mathrm{e}}^{2}}$

83.

A regular polygon of n sides has 170 diagonals,then n is equal to

• 12

• 17

• 20

• 25

84.

A committee of 12 members is to be formed from 9 women and 8 men. The number of committees in which the women are in majority is

• 2720

• 2702

• 2270

• 2278

85.

In an entrance test there are multiple choice questions. There are four possible answers to each question, of which one is correct. The probability that a student know the answer to a question is 9/10. If he gets the correct answer to a question, then the probability that he was guessing is

• $\frac{37}{40}$

• $\frac{1}{37}$

• $\frac{36}{37}$

• $\frac{1}{9}$

86.

There are four machines and it is known that exactly two of them are faulty. They are teste done by one, in a random order till both the faulty machines are identified. Then, the probability that only two tests are need is

• $\frac{1}{3}$

• $\frac{1}{6}$

• $\frac{1}{2}$

• $\frac{1}{4}$

87.

A random variable X has the probability distribution given below.
 X 1 2 3 4 5 P(X = x) K 2K 3K 2K K

Its variance is

• $\frac{16}{3}$

• $\frac{4}{3}$

• $\frac{5}{3}$

• $\frac{10}{3}$

88.

A six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be 7. The probability that the number 3 has appeared atleast once, is

• $\frac{1}{5}$

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{4}$

89.

If A, B and C are mutually exclusive and exhaustive events of a random experiment such that P(B) = $\frac{3}{2}$P(A) and P(C) = $\frac{1}{2}$P(B), then P(A ∪ C) equals to

• $\frac{10}{13}$

• $\frac{3}{13}$

• $\frac{6}{13}$

• $\frac{7}{13}$

90.

The letters of the word 'QUESTION' are arranged in a row at random. The probability that there are exactly two letters between Q and S is

• $\frac{1}{14}$

• $\frac{5}{7}$

• $\frac{1}{7}$

• $\frac{5}{28}$